10 Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress and Capillarity Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay In-place densification of granular soils Blasting or by Explosives The range of soil grain sizes suitable for compacting by blasting method is the same as for Vibroflotation. In this method, the compaction is achieved by successive detonations of small explosive charges in saturated soils. Relative densities of 70 to 80 % upto a depth of 20 to 25 m can be achieved. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Blasting or by Explosives Explosive charges (60 % dynamite, 30% special gelatin dynamite, and ammonite are most commonly used) are placed at about 2/3 times the thickness of the stratum to be densified. The spacings of the charges vary from 3 to 8 m. Three to five successive detonations of several spaced charges are usually required to achieve the desired compaction. The shock waves due to blasting cause liquefaction of the saturated sand, followed by densification. Practically no compaction is achieved in the top 1 m and so this zone usually needs recompaction by rollers. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Blasting or by Explosives The relation for the weight of charge and the sphere of influence for compaction can be given by: W = CR3 Where W = Weight of charge R = Sphere of influence C = Constant (0.0025 for 60 % dynamite) If blasting is used in dry or partially saturated soils, preflooding is desirable. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Compaction by Pounding, Dynamic compaction or High energy impact Used for improving surface and near surface zones of soil and fill material whose existing condition is considered marginal or inadequate foundation support… The method consists of dropping a heavy weight from a relatively great height; Weights ranging: 2 tons to 15 tons, and drops have ranged from 10 to 30 m. Pounding– Repeated heavy blows Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Dynamic compaction Usually, a closely spaced grid pattern is selected for the pounding locations, and the multiple poundings are required at each drop location (typically 5 to 10 drops). Can densify loose cohesion-less soils, fracture and densify buried building rubble such as that which exists at old building sites, consolidate fine grained soils, and compact buried garbage fills. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay The pounding creates a depression at each drop location and also produces an areal settlement. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Water table Air in irregular spaces between soil particles Water surrounding particles and at points of contact between particles, and filling small void spaces Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay A soil can be visualized as a skeleton of solid particles enclosing continuous voids which contain water and / or air. The volume of the soil skeleton as a whole can change due to rearrangement of the soil particles into new positions, mainly by rolling and sliding, with a corresponding change in the forces acting between the particles. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay In a fully saturated soil, since water is considered to be incompressible, a reduction in volume is possible only if some of the water can escape from the voids. In a dry or a partially saturated soil a reduction in volume is always possible due to compression of the air in the voids, provided there is a scope for particle rearrangement. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Vertical subsurface stress resulting from the soil mass Ground surface z σv γt = unit weight of soil, homogeneous from ground surface to depth z Unit area σv = γt z Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Pore pressure Pore water pressure (PWP) is the pressure in the water in the void spaces or pores which exist between and around the mineral grains. • u = pore pressure pore water u grains u u u u Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Pore pressure Pore water pressure under no flow conditions is given by the hydrostatic pressure. ground surface u = γw h WT pore water h grains Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Pore Water Pressure As the name implies, is the pressure which exists in the water which is present in the pores of the soil. The soil pores are normally interconnected and they may be visualized as being a highly intricate and complex collection of irregular tubes. z γw z Soil having interconnected voids which are similar to irregular tubes… Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress principle (Karl Terzaghi in 1936) Valid only for Saturated soils Effective stress σ´ , at a point in a soil mass is equal to the total stress σ, at that point minus the pore water pressure u, at that location. σ ′ = σ − uw Both total stress σ and pore water pressure u are physically meaningful parameters; stresses that can actually be measured in the field. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Terzaghi’s Effective Stress Principle • Terzaghi (1936) proposed the relationship for effective stress. • “All measurable effects of a change of stress, such as compression, distortion, and a change of shearing resistance are due to changes in effective stress”. • Certain aspect of the engineering behaviour of soil, especially, compression and shear strength are functions of effective stress. First important equation in Geotechnical Engineering… Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Nature of effective stress Effective stress σ´, by definition, can be determined only by arithmetic manipulation: σ - uw Unlike σ and uw, σ´ is thus not a physical parameter. It is thus only a mathematical concept but obviously a useful parameter since it has empirically been observed to be the determinant of the engineering behaviour of soil. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress concept through an idealized saturated soil element under stress σ A grains σ A′′ A′′ ’′ ′ A A F′ uw A Pore water w Ac An idealized saturated soil element in equilibrium A′′A′′ is stretched view of plane A′A′ • Wavy plane A´A´ passes through particle to particle points – almost entire plane passes through pore water Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress concept through an idealized saturated soil element under stress A σ Since the soil element is in equilibrium the algebraic ′′ A′′ sum of the forces must be A equal to zero. F′ uw Aw Ac σA The total stress on account of overburden, σ, multiplied by the area of plane A uwAw The pore water pressure multiplied by the area of the plane which passes through pore water Aw F´ The summation of forces which act at particle to particle contacts through which the plane passes. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective Stress Effective stress is not • Applying laws of statics to the stress at particle to soil element in equilibrium particle contact. Stress at particle • Ac + Aw = A contact is a physical • σA = F′ + uw (Aw) stress equal to F′/(Ac) • σ = (F′/A) + [uw (A-Ac)/A] Where a = contact area • σ = σ′ + (1-A /A) u c w between particles per unit • σ = σ′ + (1-a) uw gross area of the soil. In granular materials a → 0, σ ′ = σ − u [After Lambe and Whitman, 1969] w Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress concept At point O σ = γh1 + γ sat h2 Point O a) Gross area A uw = γ wh2 Area of contact b) soil solid Total Area of contact soil solid = A σ ′ = γh1 + γ subh2 c c) Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress is sometimes used interchangeably with intergranular stress. Although the terms are approximately same, there is some difference. Total vertical force F at the level of O is the sum of the following forces: 1)Forces carried by soil solids at their point of contact Fs Fs = F1(v) + F2(v) + F3(v)+…. Vertical components of F1, F2,.. 2)Force carried by water Fw = uw(A-Ac) 3)Electrical attractive force between solid particles at the level of O, FA 4) Electrical repulsive force between solid particles at the level of O, FR Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress concept Total Vertical force F = Fs+ Fw - FA+ FR A σ = σ + u 1− c − A′ + R′ ig w A σ = σ ig + uw (1− a)− A′ + R′ Where σig = intergranular stress; a = Ac/A ; A´ = Electrical attractive force per unit area of cross-section of soil; R´ = Electrical repulsive force per unit area of cross-section of soil. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Intergranular Stress Hence σ ig = σ − uw (1− a)+ A′ − R′ The value of a is very small in the working stress range.. a 0 σ ig = σ − uw + A′ − R′ For granular soils, silts, and clays of low plasticity, the magnitudes of A´ and R´ are small; For all practical purposes, the intergranular stress becomes: σ ig ≈ σ − uw Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Intergranular Stress In highly plastic and dispersed clays, A´ - R´ is large, such situations: σ ig ≠ σ − uw In clay soils mineral crystals are not in direct contact since they are surrounded by adsorbed layers of water.